Expression for vertical deflection in a cathode ray tube

This can be used to calculate the deflection of the beam on the screen based on the accelerating and deflecting voltages, the effective length of the deflecting plates, the distance from the end of the plates to the screen, the distance between plates, the mass and charge of the electron. It is important to show working and understand the expression in order to accurately perform the experiment.
  • #1
Yura
39
0
i need to find the expression for the vertical direction of a beam in a cathode ray tube, using:
Va - accelerating voltage (between cathode &anode)
Vd - deflecting voltage
ly - effective length of deflecting plates
L - distance from end of plates to the screen
d - distance between plates
Me - mass of electron
e - charge of electron

this is for a prac of mine so i need to work it out during the prac and show working and everything, but i would like to know what the expression looks like so i have a general idea of what I am doing and can see if i get something wrong.

thanks.
 
Physics news on Phys.org
  • #2
The expression for the vertical direction of a beam in a cathode ray tube is:Vd * ly / (Me * e * L) * (Va - Vd) * d
 
  • #3


The expression for vertical deflection in a cathode ray tube can be calculated using the following formula:

y = (Va * Vd * ly * L) / (d * Me * e)

Where:
y = vertical deflection in meters
Va = accelerating voltage between cathode and anode in volts
Vd = deflecting voltage in volts
ly = effective length of deflecting plates in meters
L = distance from end of plates to the screen in meters
d = distance between plates in meters
Me = mass of electron in kilograms
e = charge of electron in coulombs

To show the working, we can break down the formula into smaller steps:

Step 1: Calculate the electric field between the deflecting plates using the deflecting voltage:
E = Vd / d

Step 2: Calculate the force acting on an electron in the electric field:
F = E * e

Step 3: Calculate the acceleration of the electron:
a = F / Me

Step 4: Calculate the time taken for the electron to travel from the deflecting plates to the screen:
t = sqrt (2 * L / a)

Step 5: Calculate the vertical deflection of the electron on the screen:
y = (1/2) * a * t^2

Substituting the values from steps 1-4 into step 5, we get:

y = (1/2) * (F / Me) * (sqrt (2 * L / (F / Me)))^2

Simplifying, we get:

y = (Va * Vd * ly * L) / (d * Me * e)

Therefore, the expression for vertical deflection in a cathode ray tube is:

y = (Va * Vd * ly * L) / (d * Me * e)

I hope this helps and good luck with your experiment!
 

1. What is the expression for vertical deflection in a cathode ray tube?

The expression for vertical deflection in a cathode ray tube is given by the equation: y = kVd, where y is the vertical deflection, k is the sensitivity constant, and Vd is the applied voltage.

2. How is the sensitivity constant determined for a cathode ray tube?

The sensitivity constant for a cathode ray tube is determined by measuring the distance between the center of the screen and the top and bottom edges, and then dividing that distance by the voltage applied to the deflection plates.

3. Can the expression for vertical deflection be used for all types of cathode ray tubes?

Yes, the expression for vertical deflection can be used for all types of cathode ray tubes, as long as the sensitivity constant is properly determined for each tube.

4. How does the applied voltage affect the vertical deflection in a cathode ray tube?

The applied voltage directly affects the vertical deflection in a cathode ray tube. As the voltage increases, the deflection also increases, causing the electron beam to move further up or down on the screen.

5. What is the purpose of the vertical deflection in a cathode ray tube?

The purpose of the vertical deflection in a cathode ray tube is to control the placement of the electron beam on the screen, allowing for the creation of images or patterns. This is an important component in the functioning of a cathode ray tube, such as in a television or computer monitor.

Similar threads

  • Introductory Physics Homework Help
2
Replies
44
Views
10K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
17
Views
1K
  • Quantum Physics
Replies
2
Views
801
  • General Engineering
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
830
Back
Top